The Bayesian statement is a conditional one: Given something which is known, namely the data from our experiment, a degree of certainty is expressed about something which is unknown, namely the value of ψ. The sampling theory statement is also, according to a Bayesian at least, conditional, but the wrong conditioning is taking place. It is the unknown parameter value that is taken as given, rather than the known data. Indeed, as noted, the connection of the sampling theory statements to the data at hand is, at best, a tenuous one. It is not at all clear what one is supposed to think about a given computed interval from a sampling point of view. For the Bayesian, on the other hand, all attention is focused on the given interval, which refers directly to a posterior belief distribution. Results of future sampling or references to sampling distributions are irrelevant from this point of view.
To conclude, the difference between Bayesian and sampling theory statements may be stated even more sharply than before: Bayesian statements are directly relevant to the questions researchers ask. Sampling theory statements are not only indirect but of questionable relevance. Given this difference, the question posed earlier in this section may be rephrased. Why should anyone not switch from making sampling theory statements to making Bayesian ones?
Bock, R. D. ( 1975). Multivariate statistical methods in behavioral research. New York: McGrawHill.
Box, G. E. P., & Tiao, G. C. ( 1973). Bayesian inference in statistical analysis. Reading, MA: Addison-Wesley.
Dunn, O. J. ( 1961). "Multiple comparisons among means". Journal of the American Statistical Association, 56, 52-64.
Edwards, W., Lindman, H., & Savage, L. J. ( 1963). "Bayesian statistical inference for psychological research". Psychological Review, 70, 193-242.
Finn, J. D. ( 1978). User's guide. MULTIVARIANCE: Univariate and multivariate analysis of variance, covariance, regression and repeated measures. Chicago: National Educational Resources.
Finn, J. D., & Mattsson, 1. ( 1978). Multivariate analysis in educational research. Applications of the MULTIVARIANCE program. Chicago: National Educational Resources.
Keppel, G. ( 1973). Design and analysis: A researcher's handbook. Englewood Cliffs, NJ: PrenticeHall.
Kirk, R. E. ( 1982). Experimental design: Procedures for the behavioral sciences ( 2nd ed.). Belmont, CA: Brooks/Cole.
Mosteller, F., & Tukey, J. W. ( 1977). Data analysis and regression: A second course in statistics. Reading, MA: Addison-Wesley.
Novick, M. R., Hamer, R. M., Libby, D. L., Chen, J. J., & Woodworth, G. C. ( 1980). Manual for the computer-assisted data analysis (CADA) monitor-1980. Iowa City, IA: University of Iowa.
Novick, M. R., & Jackson, P. H. ( 1974). Statistical methods for educational and psychological research. New York: McGraw-Hill.
Tukey, J. W. ( 1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
Woodworth, G. C. ( 1979). "Bayesian full rank MANOVA/MANCOVA: An intermediate exposition with interactive computer examples". Journal of Educational Statistics, 4, 357-404.